Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

<image>

In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.util.*;
public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int m = sc.nextInt();
		
		int [][] arr = new int[n][m];
		
		for (int i=0;i<n;i++)
			for (int j=0;j<m;j++)
				arr[i][j] = sc.nextInt();
		
		int [] r = new int[n];
		int [] c = new int[m];
		boolean flag = true;
		if (n<=m)
		{
			Arrays.fill(r, Integer.MAX_VALUE);
			
			for (int i =0;i<n;i++)
			{
				for (int j =0;j<m;j++)
				{
					if (arr[i][j]<r[i])
						r[i] = arr[i][j];
					
				}
			}
			
			for (int i =0;i<n;i++)
				for (int j =0;j<m;j++)
					arr[i][j]-=r[i];
			
			for (int i =0;i<m;i++)
			{
				if (arr[0][i]!=0)
				{
					c[i]=arr[0][i];
					for (int j=0;j<n;j++)
						arr[j][i]-=c[i];
				}
			}
			
		}
		else
		{
			Arrays.fill(c, Integer.MAX_VALUE);
			
			for (int i =0;i<m;i++)
			{
				for (int j =0;j<n;j++)
				{
					if (arr[j][i]<c[i])
						c[i] = arr[j][i];
					
				}
			}
			
			for (int i =0;i<m;i++)
				for (int j =0;j<n;j++)
					arr[j][i]-=c[i];
			
			for (int i =0;i<n;i++)
			{
				if (arr[i][0]!=0)
				{
					r[i]=arr[i][0];
					for (int j=0;j<m;j++)
						arr[i][j]-=r[i];
				}
			}
			
			
		}
		
		for (int i =0;i<m;i++)
		{
			for (int j =0;j<n;j++)
			{
				if (arr[j][i]!=0)
				{
					flag=false;
					break;
				}
				
				
			}
			if (!flag)
				break;
		}
		
		if (flag)
		{
			ArrayList<String> ar = new ArrayList<String>();
			for (int i =0;i<n;i++)
			{
				if (r[i]>0)
				{
					while(r[i]>0)
						{
							ar.add("row "+(i+1));
							r[i]--;
						}
				}
			}
			for (int j =0;j<m;j++)
				if (c[j]>0)
					while(c[j]>0)
					{
						ar.add("col "+(j+1));
						c[j]--;
					}
			
			System.out.println(ar.size());
			for (int i=0;i<ar.size();i++)
				System.out.println(ar.get(i));
		}
		else
			System.out.println(-1);
		
		sc.close();

	}

}